Chromatic dispersion compensating optical fiber

ABSTRACT

The invention relates to the field of single-mode chromatic dispersion compensating optical fibers for a wavelength multiplexing transmission network. A single-mode chromatic dispersion compensating optical fiber is provided having at least six core slices ( 1  to  6 ) and having a negative chromatic dispersion and chromatic dispersion slope at a central wavelength.

The invention relates to the field of chromatic dispersion compensatingoptical fibers for wavelength multiplexing transmission networks.

According to the prior art, a dispersion compensating optical fiber, fora group of optical properties such as the chromatic dispersion, thechromatic dispersion slope and the effective surface, has a centralslice whose maximum index is very high, essentially in order to ensure ahigh absolute value for negative chromatic dispersion of the chromaticdispersion compensating optical fiber.

To improve the total compromise between on one hand the group of opticalproperties of the chromatic dispersion compensating optical fiber and onthe other hand its cost, essentially related to the difficulty andcomplexity of its fabrication process, the invention proposes to modifythe balance between the difficulty of the process and the complexity ofthe process. It is indeed proposed by the invention to add core slicesto the chromatic dispersion compensating optical fiber of a line opticalfiber, to increase the number of core slices of a dispersioncompensating optical fiber from four to at least six, what certainlyincreases the complexity of the process by adding at least two slicesbut at the same facilitates this process since it enables a considerablereduction in the maximum doping value of the central slice making iteasier to fabricate. The chromatic dispersion compensating optical fibermay in fact have more slices but these are in total easier to produce.By increasing the number of slices while reducing the maximum value ofthe doping level of the central slice it is possible to reduce theattenuation and the polarisation mode dispersion while increasing theeffective surface area, which relates to a better total compromisebetween the group of optical properties of the chromatic dispersioncompensating optical fiber according to the invention.

According to the invention, a single-mode chromatic dispersioncompensating optical fiber is provided for a wavelength multiplexingtransmission network, having a chromatic dispersion C at a centralwavelength of the spectral band used which is less than −50 ps/nm-km,having a chromatic dispersion slope C′ at said central wavelength whichis negative, having a ratio of chromatic dispersion to the chromaticdispersion slope C/C′ at said central wavelength which is less than 600nm, and successively comprising, from the center towards the periphery,a core having a variable index profile and then a cladding of constantindex, characterized in that the variable index profile of the corecomprises at least six slices among which successively, from the centertowards the periphery, a central slice whose maximum index is greaterthan the index of the cladding, the difference Dn1 between the maximumindex of the central slice and the index of the cladding being greaterthan 13.10⁻³, a first burried slice whose minimum index is lower thanthe index of the cladding, the difference Dn2 between the minimum indexof the first burried slice and the index of the cladding being less than−4.10⁻³, a first annular slice whose maximum index is greater than theindex of the cladding and less than the maximum index of the centralslice, the difference Dn3 between the maximum index of the first annularslice and the index of the cladding being greater than 2.5.10⁻³, asecond burried slice whose minimum index is lower than the index of thecladding, the difference Dn4 between the minimum index of the secondburried slice and the index of the cladding being less than −2.10⁻³, asecond annular slice whose maximum index is greater than the index ofthe cladding and less than the maximum index of the central slice, thedifference Dn5 between the maximum index of the second annular slice andthe index of the cladding being greater than 2.10⁻³, a third burriedslice whose minimum index is lower than the index of the cladding, thedifference Dn6 between the minimum index of the third burried slice andthe index of the cladding being less than −1.10⁻³. The choice of amaximum threshold for the ratio between chromatic dispersion andchromatic dispersion slope allows for efficient compensation of a lineoptical fiber in a wavelength multiplexing optical transmission system.This ratio is preferably chosen to be less than 500 nm, evenadvantageously less than 400 nm, at the central wavelength of thespectral band used. A spectral band used is generally at least one ofthe spectral bands S, C, L and U in which one or more optical signalsare conveyed by the line optical fiber and by the chromatic dispersioncompensating optical fiber. The spectral band S extends fromapproximately 1465 nm to 1530 nm, the spectral band C extends fromapproximately 1530 nm to 1570 nm, the spectral band L extends fromapproximately 1570 nm to 1625 nm, the spectral band U extends fromapproximately 1625 nm to 1675 nm.

Preferably, for further improvement in the total compromise between thegroup of optical properties, one or more or all the index differences ofthe six first slices are more pronounced. The difference Dn1 between themaximum index of the central slice and the index of the cladding mayadvantageously be greater than 15.10⁻³. The difference Dn2 between theminimum index of the first burried slice and the index of the claddingmay advantageously be less than −5.10⁻³. The difference Dn3 between themaximum index of the first annular slice and the index of the claddingmay advantageously be greater than 3.10⁻³. The difference Dn4 betweenthe minimum index of the second burried slice and the index of thecladding may advantageously be less than −3.10⁻³. The difference Dn5between the maximum index of the second annular slice and the index ofthe cladding may advantageously be greater than 2.5.10⁻³. The differenceDn6 between the minimum index of the third burried slice and the indexof the cladding may advantageously be less than −2.10⁻³.

In order to further improve the total compromise between the group ofoptical properties of the chromatic dispersion compensating opticalfiber, the invention proposes two quality factors, the first qualityfactor adapted to a chromatic dispersion compensating optical fiberintended to compensate a standard single mode optical fiber (SSMF) whichcorresponds to a ratio between chromatic dispersion and chromaticdispersion slope that is relatively high, typically between 250 nm and400 nm, and the second quality factor being adapted to a chromaticdispersion compensating optical fiber intended to compensate a non-zerodispersion shifted line optical fiber (NZ-DSF) which corresponds to aratio between chromatic dispersion and chromatic dispersion slope thatis relatively low, typically less than 200 nm.

In a first preferred embodiment, to compensate a standard single modeline optical fiber having a central slice with a radius r₁ and a firstburried slice with a radius r₂, the chromatic dispersion compensatingoptical fiber has a first quality factor Q1 that is positive and lessthan 90 nm-km/ps-μm⁴, wherein:

${Q1} = {{- 4800}\frac{\left( {{Dn1} - {Dn2}} \right)^{3/2}}{C \cdot \left( r_{1} \right)^{2} \cdot \left( r_{2} \right)^{2}}}$

the radii r₁ and r₂ being expressed in μm, the chromatic dispersion Cbeing expressed in ps/nm-km, the index differences Dn1 and Dn2 beingexpressed without unit but multiplied by a factor of one thousand. In aneven more advantageous embodiment, the first quality factor Q1 ispositive and less than 80 nm-km/ps-μm⁴, even positive and less than 70nm-km/ps-μm⁴, even positive and less than 60 nm-km/ps-μm⁴.

In a second preferred embodiment, to compensate a non-zero dispersionshifted line optical fiber in the spectral band used having a centralslice with a radius r₁ and a first burried slice with a radius r₂, thechromatic dispersion compensating optical fiber has a second qualityfactor Q2 that is positive and less than 100 km/ps-μm^(1/2), wherein:

${Q2} = {12800\frac{{Dn1} \cdot {Dn2} \cdot C^{\prime}}{\left( r_{1} \right)^{1/2} \cdot (C)^{2}}}$

the radius r₁ being expressed in μm, the chromatic dispersion C beingexpressed in ps/nm-km, the chromatic dispersion slope C′ being expressedin ps/nm²-km, the index differences Dn1 and Dn2 being expressed withoutunit but multiplied by a factor of one thousand. In a furtheradvantageous embodiment the second quality factor Q2 is positive andless than 90 km/ps-μm^(1/2), even positive and less than 80km/ps-μm^(1/2).

In one embodiment the chromatic dispersion compensating optical fiber ofthe invention has a variable index profile of the core whichsuccessively comprises, from the center towards the periphery, at leasteight slices among which the six slices of the embodiment describedabove, i.e. two annular slices and three buried slices, and towards theperiphery additionally comprising a third annular slice whose maximumindex is greater than the index of the cladding and less than themaximum index of the central slice, a fourth burried slice whose minimumindex is less than the index of the cladding.

In a further embodiment, the chromatic dispersion compensating opticalfiber of the invention has a variable index profile of the core whichsuccessively comprises, from the center towards the periphery, at leastten slices among which the six slices of the embodiment described above,i.e. two annular slices and three buried slices, and the two furtherslices of the embodiment directly above, i.e. a third annular slice anda fourth burried slice, and towards the periphery additionallycomprising a fourth annular slice whose maximum index is greater thanthe index of the cladding and less than the maximum index of the centralslice, a fifth burried slice whose minimum index is less than the indexof the cladding.

Preferably, for even further improved efficiency in chromatic dispersioncompensation of the line optical fiber, the chromatic dispersioncompensating optical fiber of the invention has a chromatic dispersionwhich is less than −80 ps/nm-km, even less than −120 ps/nm-km.

The invention also concerns a chromatic dispersion compensating modulecomprising at least one chromatic dispersion compensating optical fiberaccording to the invention. The first and second quality factors areparticularly well adapted to dispersion compensating optical fibers(DCF) intended to be placed in a module, which corresponds to a rathernegative dispersion, i.e. typically less than −50 ps/nm-km, in contrastto dispersion compensating optical fibers intended to be placed in acable (reverse dispersion fiber: RDF) which corresponds to a moderatelynegative dispersion, i.e. typically between −10 ps/nm-km and −50ps/nm-km.

The invention will be better understood and other characteristics andadvantages will become apparent on reading the following description andits appended drawings given as examples in which:

FIG. 1 is a diagram showing an example of a profile type having tenslices of a chromatic dispersion compensating optical fiber according tothe invention,

FIG. 2 is a table giving the values for the radii and index differencesfor two examples of profiles with six slices of a chromatic dispersioncompensating optical fiber according to the invention, intended tocompensate a standard single mode optical fiber;

FIG. 3 is table giving certain characteristics of profiles of chromaticdispersion compensating optical fibers according to the inventiondefined in FIG. 2;

FIG. 4 is a table giving the values of the radii and index differencesfor two examples of profiles having eight slices of a chromaticdispersion compensating optical fiber according to the invention,intended to compensate a standard single mode optical fiber;

FIG. 5 is a table giving certain profile characteristics of a chromaticdispersion compensating optical fiber according to the invention definedin FIG. 4;

FIG. 6 is a table giving the values of the radii and index differencesfor an example of a profile having ten slices of a chromatic dispersioncompensating optical fiber according to the invention, intended tocompensate a standard single mode optical fiber;

FIG. 7 is a table giving certain characteristics of profiles of achromatic dispersion compensating optical fiber according to theinvention as defined in FIG. 6;

FIG. 8 is a table giving the values of the radii and index differencesof two examples of profiles having six slices of a chromatic dispersioncompensating optical fiber according to the invention, intended tocompensate a non-zero dispersion shifted optical fiber in the spectralband used;

FIG. 9 is a table giving certain characteristics of profiles of thechromatic dispersion compensating optical fiber according to theinvention defined in FIG. 8;

FIG. 10 is a table comprising values of the radii and index differencesof two examples of profiles having eight slices of a chromaticdispersion compensating optical fiber according to the invention,intended to compensate a non-zero dispersion shifted optical fiber inthe spectral band used;

FIG. 11 is a table giving certain characteristics of profiles of achromatic dispersion compensating optical fiber according to theinvention as defined in FIG. 10;

FIG. 12 is a table giving values of the radii and index differences foran example of a profile having ten slices of a chromatic dispersioncompensating optical fiber according to the invention, intended tocompensate a non-zero dispersion shifted optical fiber in the spectralband used;

FIG. 13 is a table giving certain characteristics of profiles of achromatic dispersion compensating optical fiber according to theinvention as defined in FIG. 12.

FIG. 1 schematically shows an example of a profile type having tenslices of a chromatic dispersion compensating optical fiber according tothe invention. For a trapezoid shape, the first slice 1, called centralslice, has a maximum index difference Dn1 with the constant index of thecladding and an outer radius r1 b. The maximum index difference Dn1 ispositive. The maximum index difference of a slice corresponds firstlyfor the central slice and the annular slices to the difference betweenthe maximum index of the slice and the constant index of the cladding,and secondly for the burried slices to the difference between theminimum index of the slice and the constant index of the cladding.Preferably, between a zero radius and the radius r1 a the index isconstant and maximum, it becomes equal to that of the cladding for avalue r1 of the radius and reaches that of the second slice for a valuer1 b. With a rectangular shape, the first slice, called central slice,has a maximum index difference Dn1 with the constant index of thecladding and an outer radius r1: in this case r1 a=r1=r1 b. The maximumindex difference Dn1 is positive. Preferably, between a zero radius andthe radius r1 the index is constant. The central slice, like every otherannular or burried slice may have various shapes including rectangular,trapezoid, alpha, irregular or any other shape or even consist ofseveral pieces (each piece possibly having any shape) some with apositive index and others with a negative index, provided that each ofthese slices respects the definition corresponding to it in claim 1. Thesecond slice 2, called first burried slice, has a maximum indexdifference Dn2 with the constant index of the cladding and an outerradius r2. The maximum index difference Dn2 is negative. Preferably,between radius r1 and radius r2 the index is constant. The third slice3, called first annular slice, has a maximum index difference Dn3 withthe constant index of the cladding and an outer radius r3. The maximumindex difference Dn3 is positive. Preferably, between radius r2 andradius r3 the index is constant. The fourth slice 4, called secondburried slice, has a maximum index difference Dn4 with the constantindex of the cladding and an outer radius r4. The maximum indexdifference Dn4 is negative. Preferably, between radius r3 and radius r4the index is constant. The fifth slice 5, called second annular slice,has a maximum index difference Dn5 with the constant index of thecladding and an outer radius r5. The maximum index difference Dn5 ispositive. Preferably, between radius r4 and radius r5 the index isconstant. The sixth slice 6, called third burried slice, has a maximumindex difference Dn6 with the constant index of the cladding and anouter radius r6. The maximum index difference Dn6 is negative.Preferably, between radius r5 and radius r6 the index is constant. Theseventh slice 7, called third annular slice, has a maximum indexdifference Dn7 with the constant index of the cladding and an outerradius r7. The maximum index difference Dn7 is positive. Preferably,between radius r6 and radius r7 the index is constant. The eighth slice8, called fourth burried slice, has a maximum index difference Dn8 withthe constant index of the cladding and an outer radius r8. The maximumindex difference Dn8 is negative. Preferably, between radius r7 andradius r8 the index is constant. The ninth slice 9, called fourthannular slice, has a maximum index difference Dn9 with the constantindex of the cladding and an outer radius r9. The maximum indexdifference Dn9 is positive. Preferably, between radius r8 and radius r9the index is constant. The tenth slice 10, called fifth burried slice,has a maximum index difference Dn10 with the constant index of thecladding and an outer radius r10. The maximum index difference Dn10 isnegative. Preferably, between radius r9 and radius r10 the index isconstant. The cladding g of constant index is found beyond radius r10.An optical fiber whose core has only eight slices corresponds to thecase in which Dn10=Dn9=0 and r10=r9=r8. An optical fiber whose core hasonly six slices corresponds to the case in which Dn10=Dn9=Dn8=Dn7=0 andr10=r9=r8=r7=r6. The core of the optical fiber preferably has an evennumber of slices even though it may possibly have 7, 9, 11 or moreslices.

FIG. 2 is a table giving values of radii and index differences for twoexamples of profiles having six slices of a chromatic dispersioncompensating optical fiber of the invention intended to compensate astandard single mode optical fiber. The left column comprises thedenomination of examples N6T1 and N6T2. The next column expresses onethousand times the index difference Dn1 (without unit). The next columnexpresses in μm the radius r1a of the variable index profile of thecore. The next column expresses in μm the radius r1 of the variableindex profile of the core. The next column expresses in μm the radius r1b of the variable index profile of the core. The next column expressesone thousand times the index difference Dn2 (without unit). The nextcolumn expresses in μm the radius r2 of the variable index profile ofthe core. The next column expresses one thousand times the indexdifference Dn3 (without unit). The next column expresses in μm radius r3of the variable index profile of the core. The next column expresses onethousand times the index difference Dn4 (without unit). The next columnexpresses in μm the radius r4 of the variable index profile of the core.The next column expresses one thousand times the index difference Dn5(without unit). The next column expresses in μm the radius r5 of thevariable index profile of the core. The next column expresses onethousand times the index difference Dn6 (without unit). The next columnexpresses in μm the radius r6 of the variable index profile of the core.

FIG. 3 is a table giving certain profile characteristics of a chromaticdispersion compensating optical fiber of the invention as defined inFIG. 2. The left column compromises the denomination of examples N6T1 anN6T2. For each example considered, the other columns representcharacteristics of the optical fiber corresponding to the example underconsideration. The next column gives the chromatic dispersion Cexpressed in ps/nm-km at a wavelength of 1550 nm. The spectral band usedis the C spectral band extending from approximately 1530 nm to 1570 nm.The next column gives the ratio between the chromatic dispersion C andthe chromatic dispersion slope C′ expressed in nm at a wavelength of1550 nm. The next column gives the radius of the WO2 mode according tothe definition of Petermann II, expressed in μm, at a wavelength of 1550nm. The next column gives the effective surface area S_(eff) expressedin μm² at a wavelength of 1550 nm. The next column gives a maximumbending loss threshold expressed in dB/m at the wavelength of 1625 nmwhen wound around a sleeve having a radius of 10 mm. The next columngives the value of the first quality factor Q1 expressed innm-km/ps-μm⁴.

FIG. 4 is a table giving the values of radii and index differences fortwo examples of profiles having eight slices of a chromatic dispersioncompensating optical fiber of the invention intended to compensate astandard single mode optical fiber. The description of FIG. 4 is similarto the description of FIG. 2 except that it comprises two additionalslices for the variable core profile and different example numbers.

FIG. 5 is a table giving certain profile characteristics of a chromaticdispersion compensating optical fiber according to the invention asdefined in FIG. 4. The description of FIG. 5 is similar to thedescription of FIG. 3.

FIG. 6 is a table giving the values of radii and index differences foran example of a profile having ten slices of a chromatic dispersioncompensating optical fiber of the invention, intended to compensate astandard single mode optical fiber. The description of FIG. 6 is similarto the description of FIG. 2 except that it comprises four additionalslices for the variable core profile and different example numbers.

FIG. 7 is a table giving certain profile characteristics of a chromaticdispersion compensating optical fiber according to the invention asdefined in FIG. 6. The description of FIG. 7 is similar to thedescription of FIG. 3.

FIG. 8 is a table giving values of radii and index differences for anexample of a profile having six slices of a chromatic dispersioncompensating optical fiber of the invention intended to compensate anon-zero shifted dispersion optical fiber in the spectral band used. Theleft column comprises the denomination of example M6T1. The next columnexpresses one thousand times the index difference Dn1 (without unit).The next column expresses in μm the radius r1 of the variable indexprofile of the core. The next column expresses in μm the radius r1 b ofthe variable index profile of the core. The next column expresses onethousand times the index difference Dn2 (without unit). The next columnexpresses in μm the radius r2 of the variable index profile of the core.The next column expresses one thousand times the index difference Dn3(without unit). The next column expresses in μm the radius r3 of thevariable index profile of the core. The next column expresses onethousand times the index difference Dn4 (without unit). The next columnexpresses in μm the radius r4 of the variable index profile of the core.The next column expresses one thousand times the index difference Dn5(without unit). The next column expresses in μm the radius r5 of thevariable index profile of the core. The next column expresses onethousand times the index difference Dn6 (without unit). The next columnexpresses in μm the radius r6 of the variable index profile of the core.

FIG. 9 is a table giving certain profile characteristics of a chromaticdispersion compensating optical fiber according to the invention asdefined in FIG. 8. The left column comprises the denomination of exampleM6T1. For each example considered the other columns representcharacteristics of the optical fiber corresponding to the example underconsideration. The next column gives the chromatic dispersion Cexpressed in ps/nm-km at a wavelength of value 1550 nm. The spectralband used is the C spectral band extending from approximately 1530 nm to1570 nm. The next column gives the ratio between chromatic dispersion Cand chromatic dispersion slope C′ expressed in nm at a wavelength of1550 nm. The next column gives the radius of the WO2 mode according tothe definition of Petermann II, expressed in μm, at a wavelength of 1550nm. The next column gives the effective surface area S_(eff) expressedin μm² at the wavelength of 1550 nm. The next column gives a maximumbending loss threshold expressed in dB/m at a wavelength of 1625 nm whenconnected to a sleeve having a radius of 10 nm. The next column givesthe value of the second quality factor Q2 expressed in km/ps-μm^(1/2).

FIG. 10 is a table giving values of radii and index differences for twoexamples of profiles having eight slices of a chromatic dispersioncompensating optical fiber of the invention intended to compensate anon-zero shifted dispersion optical fiber in the spectral band used. Thedescription of FIG. 10 is similar to the description of FIG. 8 exceptthat it comprises two additional slices for the variable index profileof the core and different example numbers.

FIG. 11 is a table giving certain profile characteristics of a chromaticdispersion compensating optical fiber of the invention as defined inFIG. 10. The description of FIG. 11 is similar to the description ofFIG. 9.

FIG. 12 is a table giving the values of radii and index differences foran example of a profile having ten slices of a chromatic dispersioncompensating optical fiber of the invention intended to compensate anon-zero shifted dispersion optical fiber in the spectral band used. Thedescription of FIG. 12 is similar to the description of FIG. 8 exceptthat it comprises four additional slices for the variable index profileof the core and different example numbers.

FIG. 13 is a table giving certain profile characteristics of a chromaticdispersion compensating optical fiber of the invention as defined inFIG. 12. The description of FIG. 13 is similar to the description ofFIG. 9.

1. A single-mode chromatic dispersion compensating optical fiber for awavelength multiplexing transmission network, having a chromaticdispersion C at a central wavelength of a spectral band used which isless than −50 ps/nm-km, having a chromatic dispersion slope C′ at saidcentral wavelength which is negative, having a ratio of chromaticdispersion to chromatic dispersion slope C/C′ at said central wavelengthwhich is less than 600 nm, successively comprising, from the centertowards the periphery, a core having a variable index profile, then acladding of constant index, characterized in that the variable indexprofile of the core comprises at least six slices (1 to 6) among whichsuccessively from the center towards the periphery, a central slice (1)whose maximum index is greater than the index of the cladding, thedifference Dn1 between the maximum index of the central slice and theindex of the cladding being greater than 13.10⁻³, a first burried slice(2) whose minimum index is lower than the index of the cladding, thedifference Dn2 between the minimum index of the first burried slice andthe index of the cladding being less than −4.10⁻³, a first annular slice(3) whose maximum index is greater than the index of the cladding andless than the maximum index of the central slice, the difference Dn3between the maximum index of the first annular slice and the index ofthe cladding being greater than 2.5.10⁻³, a second burried slice (4)whose minimum index is less than the index of the cladding, thedifference Dn4 between the minimum index of the second burried slice andthe index of the cladding being less than −2.10⁻³, a second annularslice (5) whose maximum index is greater than the index of the claddingand less than a maximum index of the central slice, the difference Dn5between the maximum index of the second annular slice and the index ofthe cladding being greater than 2.10⁻³, a third burried slice (6) whoseminimum index is lower than the index of the cladding, the differenceDn6 between the minimum index of the third burried slice and the indexof the cladding being less than −1.10⁻³.
 2. The chromatic dispersioncompensating optical fiber according to claim 1, characterized in thatthe chromatic dispersion compensating optical fiber is intended tocompensate a standard single-mode line optical fiber, and in that thecentral slice has a radius r1 and the first burried slice has a radiusr₂, the optical fiber having a first quality factor Q1 that is positiveand less than 90 nm-km/ps-μm⁴, wherein:${Q1} = {{- 4800}\frac{\left( {{Dn1} - {Dn2}} \right)^{3/2}}{C \cdot \left( r_{1} \right)^{2} \cdot \left( r_{2} \right)^{2}}}$the radii r₁ and r₂ being expressed in μm, the chromatic dispersion Cbeing expressed in ps/nm-km, the index differences Dn1 and Dn2 beingexpressed without unit but multiplied by a factor of one thousand. 3.The chromatic dispersion compensating optical fiber according to claim2, characterized in that the optical fiber has a first quality factor Q1that is positive and less than 80 nm-km/ps-μm⁴.
 4. The chromaticdispersion compensating optical fiber according to claim 3,characterized in that the optical fiber has a first quality factor Q1that is positive and less than 70 nm-km/ps-μm⁴.
 5. The chromaticdispersion compensating optical fiber according to claim 4,characterized in that the optical fiber has a first quality factor Q1that is positive and less than 60 nm-km/ps-μm⁴.
 6. The chromaticdispersion compensating optical fiber according to claim 1,characterized in that the chromatic dispersion compensating opticalfiber is intended to compensate a non-zero dispersion shifted lineoptical fiber in the spectral band used and in that the central slicehas a radius r₁, the optical fiber having a second quality factor Q2that is positive and less than 100 km/ps-μm^(1/2), wherein:${Q2} = {12800\frac{{Dn1} \cdot {Dn2} \cdot C^{\prime}}{\left( r_{1} \right)^{1/2} \cdot (C)^{2}}}$the radius r₁ being expressed in μm, the chromatic dispersion C beingexpressed in ps/nm²-km, the index differences Dn1 and Dn2 beingexpressed without unit but multiplied by a factor of one thousand. 7.The chromatic dispersion compensating optical fiber according to claim6, characterized in that the optical fiber has a second quality factorQ2 that is positive and less than 90 km/ps-μm^(1/2).
 8. The chromaticdispersion compensating optical fiber according to claim 7,characterized in that the optical fiber has a second quality factor Q2that is positive and less than 80 km/ps-μm^(1/2).
 9. The chromaticdispersion compensating optical fiber according to claim 1, wherein thevariable index profile of the core successively comprises, from thecenter towards the periphery, at least eight slices among which a thirdannular slice (7) whose maximum index is greater than the index of thecladding and less than the maximum index of the central slice, a fourthburried slice (8) whose minimum index is less than the index of thecladding.
 10. The chromatic dispersion compensating optical fiberaccording to claim 9, characterized in that the variable index profileof the core successively comprises, from the center towards theperiphery, at least ten slices among which a fourth annular slice (9)whose maximum index is greater than the index of the cladding and lessthan the maximum index of the central slice, a fifth burried slice (10)whose minimum index is less than the index of the cladding.
 11. Thechromatic dispersion compensating optical fiber according to claim 1,wherein chromatic dispersion is less than −80 ps/nm-km.
 12. Thechromatic dispersion compensating optical fiber according to claim 11,characterized in that chromatic dispersion is less than −120 ps/nm-km.13. A chromatic dispersion compensating module comprising at least onechromatic dispersion compensating optical fiber according to claim 1.